I am currently tasked with calculating the total flux of photons or irradiance from a flat emitter ('pixel'). Previously we measured the Luminance head-on (90 degree from the emitting surface) and calculated the illuminance assuming a lambertian emission. As it turns out the calculation fails for several of our devices because the radiation pattern is very much non-lamberian ($I(\alpha)=I_0*cos(\alpha)$ is not true anymore).
I am now trying to overcome this by measuring the Luminance (lm/sr/m^2) for several angles and integrate it over the solid angle to calculate the full illuminance. However I fail when it comes to the proper discretization of the solid angle.
I attached the equation as I can not write latex here (or can I?) and I am very thankful for any help I can get on this!
I wish you a nice day! Chris
(sorry I can not add images due to low reputation!)